Question

1. What is the final speed of the roller coaster shown in Figure, if it starts from rest at the
top of the 20.0 m hill and work done by frictional forces is negligible?
2. What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s
3. In Example 2, we calculated the final speed of a roller coaster that descended 20 m in
height and had an initial speed of 5 m/s downhill. Suppose the roller coaster had had an
initial speed of 5 m/s uphill instead, and it coasted uphill, stopped, and then rolled back
down to a final point 20 m below the start. We would find in that case that it had the
same final speed. Explain in terms of conservation of
energy
4. Does the work you do on a book when you lift it onto a shelf depend on the path taken?
On the time taken? On the height of the shelf? On the mass of the book?​

Answer 1

Answer:

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Answer 2

Answer:

1.] speed = $\sqrt {452}m/s$

Explanation:

1.] Energy of roller coaster when it is at top = Kinetic energy + potential energy

$T.E. = \frac{1}{2}mv^2 + mgh =\frac{1}{2}m(5)^2 + m(10)*20 =m(12.5+200)=212.5m$

Energy of roller coaster when it reaches bottom = $T.E.= \frac{1}{2}mv^2 + mgh=\frac{1}{2}mv^2+0=\frac{1}{2}mv^2$

As enrgy is always conserved,

we can equate the energies at the top and bottom,

$\implies 212.5 m = \frac{1}{2}mv^2\\\implies v^2=425\\v=\sqrt {425} m/s$

2.] Same as 1.]

3.] We know from conservation of energy that at all point of height the energy of the roller coaster will remain constant.

So, when the coaster starts with speed 5m/s to go up the tracks it will return with same speed at the ground level(5m/s). And, if it still goes down 20m below the start, it will attain the same kintic energy at it would have attained if coaster started at 20m above the ground to reach ground. So, speed will remain same in this case too.

4.] Work you do on a book when you lift it onto a shelf depends on the height of the shelf. It is because when the book is lifted onto a shelf its potential energy changes which only depends on the height of the shelf.

And the work done to place it on shelf is change in its potential energy.

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